Novel Formulation of the Helmholtz Integral for Calculating the Acoustic Field of Slender Axisymmetric Radiators

Abstract

The usual form of the Helmholtz integral expresses the sound pressure radiated by a vibrating body immersed in an acoustic fluid as an integral over the vibrating surface involving both normal velocity and surface pressure. These two quantities are interdependent owing to the acoustical behavior of the fluid. If the normal velocity is assumed prescribed, the surface pressure is generally unknown. The present method calculates the surface pressure, using an integral equation derived from the Helmholtz integral by restricting the “field” point to lie inside the radiator. It then uses the Helmholtz integral to compute the acoustic field. The integral equation has a regular kernel and a line domain. (Related integral equations used previously by others have singular kernels and surface domains.) A numerical iteration has been developed for solving the integral equation by desk computation. Ranges of frequency and slenderness for which the iteration converges have been determined. Extension of the method to elastic-acoustic interaction problems appears feasible. [Work performed under U. S. Office of Naval Research contract Nonr-3845(00)(X) with the David Taylor Model Basin.]